**The correct option is (a) 9.**

N is least positive integer and when a digit c is written after last digit of N, the resulting number is divisible by c.

⇒ So, (N)c / c

Least positive integer (N) which is divisible by digit c i.e. (1−9)

So possible number is

⇒ (9 × 8 × 7 × 5)c / c

Number, 9 × 8 × 7 × 5 is divisible by all the digits from 1 to 9

⇒ So, Number is 72 × 35 = 2520 = N

⇒ Sum of the digits of number N = 2 + 5 + 2 + 0 = 9